How Can A Paradox Exist?

Intuitively, it is of course difficult for us to grasp the notion of the contradictory. That's because we do not experience the world through Propositional Logic. Strictly speaking, contradiction can only obtain in a realm where Tautologies exist. A = -(-A)
The denial of which, truth functionally speaking, would be a contradiction. Since this does not necessarily accord with our daily life, Modal Logic was sprung on us. This takes into account truth functional variables and implicative conditionals (if...then..).
Just remember, contradiction only exists within a specific descriptive structure.

 

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Paradoxes???

Okay how about:
"I'm a Vegetarian and Work as a Butcher"
Or
"I don't clean plates, unless you pay me"

Paradoxes are on of the most tediously absurd things that occur, and fortunately a preportion of study within artificial intelligence systems that deal with Words and their contexts.

"I drempt of waking"

My personal favourite, for when someone asks you to do something and you reply...

"In a minute/second!"

"that nearly hit you!" (Is there such thing as nearly hit, it didn't hit, so it must have missed, meaning it wasn't even close to hitting you)

"If you can find proof of his guilt, we will hand him over" Taliban paradox.

"Have you ever noticed when you find what you are looking for, it's always in the last place you look!"

"I took the fish for a walk!"

"What goes up, must come down!"

I think that's all I need to type to point out there is paradoxes out there

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conceptial vs linguistic

Knowing the definition of words allows us to formulate sentences describing things that are in conflict with the conceptial templates that define the contrast between that which can be achieved and that which can not. One way to validate this claim would be to examine whether or not paradoxes existed before launguage and the written word were invented.

 

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Machaon,

Sure paradoxes exist outside of language. For example, many Escher drawings show impossible objects or impossible situations.

Cris pretty much nailed the issue:

This applies to nonverbal paradoxes as well. They are merely results of mistakes stemming from incomplete understanding or from faulty analysis.

 

I can see this topic beginning to parallel that of one of the topics involving "What do you call art?"
I checked out what Bambi had mentioned:

M.C.Escher (1898-1972) and his Artwork that spanned his life (some of which I'm sure relativity students might have studied).

rather than placing all the images that I found involving his lithographs, I'm going to place the anchors to some two sites I came across, one that is a paper about him and some of the other types of paradoxes, and the other at an Art site that you can get to see all his work (and even get extremely large versions of the image for printing)

http://www2.bc.edu/~schiavop/escher.html
A paper

http://www.artchive.com/artchive/E/escher.html
The Art gallery with poster sized versions.

I'm sure if you take a look you will realise that you've seen some of his work before, but probably didn't realise.

 

truth

in everything and everyone theres true & false, there is no 'its all inncorrect' its either true or false.

No one says im wrong, you think im wrong, send in a post.

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I disagree. There can be "degrees of truth". Those degrees are based upon the context of the arguements of truth you are interested in discovering. For example. Is it a true statement to say "stealing is wrong"? In the context of someone who has the potential to earn their living, then you could argue that stealing is wrong. But what about the context of someone who has no job, no ability to get a job, and has to support their family in some way. If their family is starving to death, is it then wrong to steal?

Truth is based on the context in which the truth is written. The truths of today are not the truths of yesterday and will probably not be the truths of tomorrow.....

 

Art and paradox.

I was one of the first people in line when the M.C. Escher exhibit came to Knoxville, Tennessee(USA). I have personally seen his works and was duly impressed by his artistic genius. However, his works demonstrate what IS possible in reference to how images are portrayed in two dimensions. They also, in my opinion, represent how it is possible for ideas to be communicated that are in conflict with what we observe about the world. The paradox arises from the fact that his art describes visually what sentences can describe verbally, they describe the ability to express that which can not be intergrated into functional ideas based on the conceptialization of reality as we can utilize it in a meaniful way. It outlines the limits of what we CAN believe against the background of what CAN be believed.

 

ON or OFF. True or false. These are facts. Everything else is grayzone stuff and excists in a state of uncertainty. Mutating and formable into whatever you like. A paradox does not excist, it is merely a idea that counteracts itself.
Loopholes in the programming of reality.
Just reboot

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How could a human be a paradox. Me in general. My teacher called me a paradox. How can this be?


The paradox definitin is a paradox by its very own definition.

 

SeekerOfTruth ...

Re. 'Degrees of Truth'

I wasn't much more than an ankle-biter when the following (more
or less) was related to me to help me understand the inter-
relatedness of 'truth', 'justice', and 'compassion' ...

The Prince, who had been captured and raised as the son of a far
distant Lord returned to his native land and unwittingly slew his
father. The law at the time required that a son who slew his
father was to be drawn and quartered.

Upon hearing the circumstances, the magistrates of the Emperor
allowed the Prince to be drawn and quartered facing the sky in
recognition of his not having known it was his father whom he
had met and slain on the field of battle.

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James R,
You write about fuzzy logic. There seems to be something fuzzy about your logic

The problem here is that "the probability that statement A is true" does not equal "the truth value of statement A".

This means that your " A statement with a value of 0.9 is mostly true." is misconceived. It should be something like " A statement with a value of 0.9 is most likely to be true."
Thus, there are still no half-truths, no so-called 'gray areas'.

I the line of machaon's remarks on Escher's work: well just as I pointed out in my earlier piece in this thread, it is all about representations. These just happen to be visual, not linguistic.

SeekerOfTruth,

Do you really think that truth is a value that is defined by the limited capabilities of those who are investigating it? This would mean that the truth is the insight one has on a particular moment.
If that were so, then there is no point in investigating. If you do not investigate, the truth is what you believe it to be.
Makes me wonder, where did you get your name?

Live long and prosper.
Merlijn

 

Descartes

Ok, far be it from me to disagree that Descartes was a crackpot, but I suddenly feel myself compelled to defend him.

Here is his argument, boiled down. He starts by assuming nothing exists, and nothing is true.

1 Thoughts are.
Edit:1.5 Thoughts are percieved through this particular stream of conciousness.
2 These thoughts whether poured into me or created myself are posessed, however transiently, by this stream of conciousness.
3 If these thoughts are pushed into this stream of conciousness by a foreign entity, I exist.
4 If these thoughts are created within this stream of conciousness, I exist.
5 If ~3 then 4.
6 If ~4 then 3.
7 Therefore, I exist.
8 Thus: I think, I am.

Generally speaking, paradoxes exist because of imperfections. Language has imperfections, so we can have bizarre statements with a true and false value. Escher can make fascinating visual paradoxes because it is not really possible to represent a three dimensional reality in a 2 dimensional projection. If anyone could build any of the things which Escher drew, that then would be a true paradox because it would have an underlying reality behind it. Words and pictures have no fundamental reality, they are tools which we use to express our understanding OF fundamental reality... I'm pretty much behind Merlijn on the rest of it.

 

Thanks Riomacleod ,

Te thing I was referring to earlier was that

is such a self referential system. The problem I wanted to point out is that the truthvalue of self referential systems cannot be determined.

Note however, that a self-referential system is paradoxal per se!
For example:

there is nothing paradoxal here.

 

No no! They are not self referential statements.

6 is not technically important to the proof, but is added to eliminate any other possibilities.

Line 5 can also read "these thoughts are either created by myself or created by something else"

Once you prove something as true, anything that logically flows from it is also true. This is why we have lemmas in mathematics.

 

James R,
I have nearly no knowledge of Fuzzy Logic. It may very well be that you are right. But then again, what do we do with it?
I for one have serious trouble with the notion of continuous truth values, I prefer the 0,1, undecided system. It's nice that the possibility of such a calculus exists, but does it add to the understanding of the nature of our universe?
I can imagine that in some (strange) multiverse theory it can provide a meaningfull description of things... I think you get my drift here. But I am not too fond of the multi-universe idea of Deutsch (and others). Even though such a theory would, I guess, in principle be able to shed some light on paradoxes.
Hmm, maybe somebody with a more thourough knowledge of the theory can tell us more about this.

Riomacleod,
'Line 5 can also read "these thoughts are either created by myself or created by something else" '
I knew what line 5 (and 6) means.... I think it is the beauty of Descartes insight.
My problem is more on a meta-level. The notions of 'thoughts', 'consciousness' and 'I' cannot be separated.
Thus, it all comes down to line/assumption (1)"Thoughts are". One cannot proof 'I' exist(S) from there, because that would mean one has to proof their assumption (1).
the notion of "I" is a thought of a consciousness. And "thoughts" are what constitutes "consciousness" (does this make sense?).
It is like "Consciouness" is a collection and "Thoughts" and "I" are elements of the collection.
It's tricky. I am going to rethink it all. I'll let you know what I have come up with.

Live long and prosper.
Merlijn

 

Hi,
it depends upon the side you first take a look.eg if you take a look at first side,where it is written the statement on other side is true,then the other side on the second look you find that NOW the statement has become false,until now it was true.the statements are interdependent and also dependent on instances you look at.
bye!.